Fiducial inference for location and scale parameters

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Abstract
Some recent papers on fiducial inference for location and scale parameters are examined from the transformation-parameter viewpoint developed in Fraser (1961a, b). For the multivariate normal case with a covariance matrix of known form, an apparent conflict between two fiducial distributions is found to be due to the inappropriate use of one of the distributions. For the multivariate normal case with an unknown covariance matrix, the Fisher-Cornish fiducial distribution for the means is apparently invalid as its derivation violates accepted rules for obtaining fiducial distributions. A fiducial distribution can, however, be developed from the transformation-parameter model and it utilizes additional structure in the form of regressions among the co-ordinates of the basic variable. The alternative fiducial distribution in Statistical Methods and Scientific Inference (Fisher, 1956) is in conflict with this transformation-parameter fiducial distribution.

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